Question

The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $1^{\circ }={\left(\frac{180}{\pi }\right)}^{\circ }\simeq {57}^{\circ },{17}^{\prime },44.8^{\prime \prime }$ and sum of interior angles of a $n$-sided regular polygon is $(2n-4)\frac{\pi }{2}$. On the basis of above information, answer the following questions :One angle of a triangle is $\frac{4x}{3}$ grades and another is $3x$ degrees, while the third is $\frac{2\pi x}{75}$ radians. Then the angles in degrees are -

• A. ${20}^{\circ },{60}^{\circ },{100}^{\circ }$
• B. ${24}^{\circ },{60}^{\circ },{96}^{\circ }$
• C. ${36}^{\circ },{60}^{\circ },{84}^{\circ }$
• D. ${20}^{\circ },{40}^{\circ },{120}^{\circ }$

Answer 1

The correct option is B ${24}^{\circ },{60}^{\circ },{96}^{\circ }$

$\frac{4x}{3}\times \frac{90}{100}+3\times \frac{2\pi \times }{75}\times \left(\frac{{180}^{\circ }}{\pi }\right)=180\Rightarrow \times ={20}^{\circ }$ angles are ${24}^{\circ },{60}^{\circ },{96}^{\circ }$